Name: solving projectile motion with components
Uploaded: 2025-05-22T09:05:40.000Z
Duration: 1 min 26 s
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K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physics

motion-and-stability-forces-and-interactions

Motion and Stability- Forces and Interactions

PS.Phy.1.2

Projectile Motion: Equations

Le mouvement d’un projectile le long des directions horizontale et verticale peut être analysé indépendamment à l’aide des équations du mouvement. En mettant ay comme moins g et unx comme zéro pour un projectile, les équations se simplifient.
Les composantes initiales de la vitesse obtenues en utilisant des relations trigonométriques simplifient encore les équations de mouvement.
Au zénith, vy est égal à zéro. En substituant vy dans l’équation de vitesse à la direction y, on obtient le temps pour le demi-vol. La hauteur zénithale du projectile peut être obtenue en substituant l’expression du temps de demi-vol dans l’équation de déplacement à la direction y.
La durée totale du vol est le double du temps du demi-vol. En substituant le temps total dans l’équation de déplacement dans la direction x, l’équation de la portée maximale du projectile est obtenue.
La trajectoire décrit la trajectoire du projectile dans un espace à deux dimensions. Son équation peut être obtenue en utilisant les équations de position.
En réarrangeant les termes de l’équation de la composante x et en les remplaçant par l’équation de la position y, nous obtenons l’équation finale de la trajectoire. Cette équation représente une parabole.

mouvement de projectile : équations

Le mouvement de projectile est couramment observé dans notre vie quotidienne. Par exemple, un joueur lançant un ballon de basket, une flèche tirée d'un arc et des enfants sautant dans la piscine, tous subissent un mouvement de projectile.

Tout problème de mouvement de projectile peut être résolu en utilisant la stratégie suivante:

<ol>
	<li>Initialement, décomposez le mouvement en composantes horizontales et verticales le long des axes x et y. Les magnitudes des composantes de déplacement le long de ces axes sont x et y. Les magnitudes des composantes verticales et horizontales de la vitesse sont données par v sin(θ) et v cos(θ), respectivement, où v est la magnitude de la vitesse et θ est sa direction par rapport à l'horizontale.</li>
	<li>Traitez le mouvement comme deux mouvements unidimensionnels indépendants: un horizontal et un vertical. Utilisez les équations cinématiques pour le mouvement horizontal et vertical présentées précédemment.</li>
	<li>Résolvez les inconnues dans les deux mouvements séparés. Notez que la seule variable commune entre les mouvements est le temps t. Les procédures de résolution des problèmes ici sont les mêmes que celles de la cinématique unidimensionnelle.</li>
	<li>Recombinez les quantités dans les directions horizontale et verticale pour trouver le déplacement et la vitesse totaux. Enfin, effectuez le calcul pour connaître la magnitude et la direction du déplacement et de la vitesse en utilisant ces équations :</li>
</ol>

<img alt="Equation1" src="/files/ftp_upload/12635/12635_Equation_1.png" style="text-align: center; height: 16px;" />

<img alt="Equation2" src="/files/ftp_upload/12635/12635_Equation_2.png" style="text-align: center; height: 26px;" />

<img alt="Equation3" src="/files/ftp_upload/12635/12635_Equation_3.png" style="text-align: center; height: 19px;" />

où θ est la direction du déplacement.

Ce texte est adapté de <a href="https://openstax.org/books/university-physics-volume-1/pages/4-3-projectile-motion">Openstax, University Physics Volume 1, Section 4.3: Projectile Motion.</a>

Mouvement de projectile : équations

Le mouvement des projectiles est couramment observé dans notre vie quotidienne. Par exemple, un ballon de basket lancé par un joueur, une flèche tirée d’un arc, et des enfants qui sautent...

Education

Enseignement

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Physique

Unit 1

Unité 1

Motion in Two or Three Dimensions

Mouvement en deux ou trois dimensions

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

solving projectile motion with components

Projectile motion can be solved by breaking the motion into horizontal and vertical components. This approach is used for common examples like a basketball throw, an arrow shot from a bow, and kids jumping into a pool. The motion is then analyzed along the x-axis and y-axis.

Start by separating displacement into x and y parts. The horizontal and vertical parts of velocity are also separated. If the projectile has speed v and direction θ relative to the horizontal, the vertical component is v·sin(θ) and the horizontal component is v·cos(θ).

Next, treat the horizontal motion and the vertical motion as two independent one-dimensional motions. Use the kinematic equations for each direction, just as in earlier one-dimensional kinematics problems. The key shared variable is time, t, so solve each part separately and use time to connect them.

After finding the unknowns, recombine the horizontal and vertical quantities to get the total displacement and velocity. Then use the combined x and y values to find the magnitude and direction of displacement and velocity. In this step, θ is the direction of the displacement.

Solving Projectile Motion with Components

solving-projectile-motion-with-components

position and displacement vectors

Describing Motion with Position Changes

Describing motion starts with position. Position tells where an object is at a particular time. It must be measured relative to a frame of reference, which is an arbitrary set of axes used to describe position and motion. Earth is often used as a frame of reference. It helps describe an object’s location in relation to stationary objects on Earth. Many important motions also take place in two dimensions, or in a plane. In those cases, position, velocity, and acceleration can each be described...

average and instantaneous velocity vectors

average-and-instantaneous-velocity-vectors

Position Change and Instant Velocity

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acceleration vectors

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projectile motion

Projectile Paths Under Gravity

Projectile motion describes the path of an object thrown into the air under Earth’s gravity. The object is called a projectile, and its curved path is called the trajectory. This motion appears in many real situations, such as fireworks, a golf ball in flight, meteors entering Earth’s atmosphere, and bullets being fired. When a falling object has no horizontal movement, it is described as one-dimensional projectile motion. When motion includes both horizontal and vertical parts, it is...

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projectile motion: equations

Projectile motion can be solved by breaking the motion into horizontal and vertical components. This approach is used for common examples like a basketball throw, an arrow shot from a bow, and kids jumping into a pool. The motion is then analyzed along the x-axis and y-axis. Start by separating displacement into x and y parts. The horizontal and vertical parts of velocity are also separated. If the projectile has speed v and direction θ relative to the horizontal, the vertical component is...

projectile motion: example

Projectile Motion in Sports and Orbit

Projectile motion helps explain both sports throws and motion near Earth. A javelin thrower uses this idea to send the javelin as far as possible. The thrower also takes a short run-up to increase the initial speed of the javelin. For a projectile on level ground, the range is the horizontal distance it travels. The range is largest at a 45° angle, so javelin throwers try to release the javelin as close to that angle as possible. In this case, the range equation assumes the distance is very...

uniform circular motion

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Uniform circular motion describes motion in a circle at constant speed. An object follows a curved path, but its speed does not change. The motion of a point on a propeller spinning at a steady rate and the second, minute, and hour hands of a watch are common examples. Even with constant speed, these objects are still accelerating. That idea can seem surprising because in one-dimensional motion, constant speed means zero acceleration. In two- and three-dimensional motion, a particle can...

non-uniform circular motion

Circular Motion with Changing Speed

Circular motion can happen with changing speed. In this case, the object still follows a circular path, but it may speed up or slow down as it moves. When speed changes during circular motion, the motion is called non-uniform circular motion. This adds tangential acceleration, which points along the path of motion and shows a change in speed. Centripetal acceleration is still present in circular motion. It describes the time rate of change of the direction of the velocity vector and points...

relative velocity in one dimension

Relative Motion in a Train and Earth

Relative motion depends on the reference frame used to measure velocity. A reference frame is the point of view from which motion is described. In many examples, Earth is the reference frame. If someone is said to be sitting in a train moving east at 10 m/s, that speed is measured relative to Earth.

relative velocity in two dimensions

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Relative velocity describes motion as measured from a chosen reference frame. It can also describe the motion of one reference frame compared with another. In two dimensions, this idea helps track how position and velocity change from frame to frame. Consider a particle P and two reference frames, S and S′. The position of the origin of S′, measured in S, and the position of P, measured in S′, can be combined with vector addition to find the position of P in S. This relation shows how motion...

key terms and concepts

Learn how to solve projectile motion by splitting motion into horizontal and vertical components, using kinematic equations, and recombining displacement and velocity.

Solving Projectile Motion with Components | JoVE K12

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JoVE Core Physique présente plusieurs branches de la physique fondamentale grâce à des vidéos animées concises et faciles à comprendre ; cela inclut: la cinématique, la dynamique, la mécanique des fluides, la mécanique statique, les ondes et l'acoustique. En parallèle, les vidéos de scientifiques à l'action démontrent l'application de concepts associés à ces domaines dans des expériences de recherche classiques et originales réalisées dans des laboratoires modernes du monde entier.

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Ohio’s Learning Standards and Model Curriculum

Motion

Projectile Motion

Tennessee Academic Standards

High School

Motion and Stability: Forces and Interactions

PHYS.PS2.4

PHYS.PS2.13

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Physical Science

PS.8

PS.8.a

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PS.Phy.2.3

Analyze the motion of objects using time, distance, displacement, speed, velocity, and acceleration.

Solving Projectile Motion with Components

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